For a homogeneous gaseous reaction `A to B + D` the initial `p_(0)` while pressure after time t was p. Derive an expression for rate constant k in terms of `p_(0),p and t`

Answer

`k=(2.303)/t log (2p_(0))/(3p_(0)-p)`

Explanation

Let the initial number of moles of `CH_(3)COOCH_(3)` be a .
`{:("Intial moles","a 0 0 0"),(CH_(3)COOCH_(3)toC_(2)H_(4)+H_(2)+CO,),("Moles after time"t : (a-x),"x x x x "):}`
According to the given data ,
` a = 0.42 ( "intial moles corresponds to 0.42 atm")`
and `{(a-x) +x+x+x} = 0.54`
`( " Mole after 6.5 min corresponds to 0.54 atm ")`
or `a+2x= 0.54`
or ` x = (0.54 - 0.42)/2 = 0.06`
Applying first - order rate equation ,
` k = (2.303)/(6.5) log. (0.42)/(0.42 - 0.06) = 0.0237 min^(-1)` .